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Graphene, a two-dimensional monatomic layer of carbon material, has demonstrated as a good candidate for applications of ultrafast photodetectors, transistors, transparent electrodes, and biosensors. Recently, many studies have shown that using metallic deep gratings could enhance the absorptance of graphene of 2.3% up to 80% in the near infrared region for applications in photon detection. This paper presents utilizing a nanograting structure, namely, a compound metallic grating could greatly enhance the absorptance of graphene up to 98% and widen its spectral bandwidth to 0.6 μm, which are greater than those of previous work. The study also showed that the absorptance spectrum is insensitive to angles of incidence. Furthermore, the proposed graphene-covered compound grating might bring a lot of benefits for graphene designs-based optical and optoelectronic devices.

Functional post-wall waveguides that are formed by periodically distributed dielectric posts are numerically analyzed. In this preliminary study, the propagation constant and attenuation constant of the dielectric post-wall waveguide is rigorously calculated using our originally developed numerical method. The developed formulation is accurate and numerically very fast. Structural parameters of the dielectric post-wall waveguide are properly chosen in order to achieve the confinement of the field in the guiding region as strong as possible even in case of one-layered dielectric structure. The final goal of our investigations is to realize the functional dielectric post-wall waveguide-based filters, which are expected to have a practical application in THz region, where the metallic (PEC) rods are losing their properties.

Purpose The purpose of this paper is to develop a rigorous self-contained formulation for analyzing electromagnetic scattering by grating of plasmonic nanorods. The authors investigate this structure from the viewpoint of the practical application as a refractive index plasmonic sensor. The presented rigorous formulation is accompanied with a neat implementation providing a high computation efficiency and could be considered as an important tool for designing and optimizing compact sensors. Design/methodology/approach Scattering of an incident plane wave by grating made of a periodic arrangement of metal-coated dielectric nanocylinders on a dielectric slab is rigorously investigated using the recursive algorithm combined with the lattice sums technique. As a dielectric slab, the authors consider glass material, which is widely used in experiments, whereas silver (Ag) is used as a low loss metal suitable to excite plasmon resonances. The main advantage of the developed self-contained formulation is that first the authors extract the reflection and transmission matrices of a single planar array from a separate analysis of the grating and the slab and then obtain the scattering characteristics of the whole structure by using a recursive formula. The method is computationally fast. Findings Dependence of the surface plasmon resonance wavelength on the refractive index of the surrounding medium is carefully investigated. The resonance peaks are red-shifted with respect to an increasing refractive index of surrounding medium showing an almost linear behavior. Near field distributions are analyzed at the resonance wavelengths of the spectral responses. Special attention is paid to the formation of the dual-absorption bands because of the excitation of the localized surface plasmons. The authors give physical insight to the coupling between grating and the glass slab. The authors found that a strong enhancement of the field inside the slab occurs when the scattered wave of the grating is phase-matched to the guided modes supported by the slab. Originality/value In the authors’ formulation, they do not use any approximation and it is rigorous and accurate. The authors use their original method. The method is based on the lattice sums technique and uses the recursive algorithm to calculate the generalized reflection and transmission characteristics by grating. Such fast and accurate method is an effective tool apt for designing and optimizing tailored sensors, for e.g. advanced biomedical applications.

Scattering of light by metal-coated dielectric nanocylinders periodically distributed along a cylindrical surface is investigated both theoretically and numerically. The structure is under the authors' interest because of its practical application in design and fabrication of plasmonic devices such as plasmonic ring resonators, Plasmonic Crystals and THz waveguides. The method is based on the T-matrix approach and the field expansion into the cylindrical Floquet modes. The method is rigorous, straightforward and can be easily applied to various cylindrical configurations with different types and locations of the excitation sources. Scattering cross section and absorption cross section of three and four silver (Ag) coated-dielectric nanocylinders periodically situated along a cylindrical surface are studied. Near field distributions are investigated at particular wavelengths corresponding to the resonance wavelengths in the spectral responses. Special attention is paid to the unique and interesting phenomena characterizing the cylindrical structure composed of the metal-coated nanocylinders such as: a ) localization of the field at the outer and inner interfaces of the metal-coated nanocylinders; b) excitement of the field in the gap region between the nanocylinders through the coupled plasmon resonance and c) strong confinement of the field inside the cylindrical structure. Detailed investigations have shown that unique phenomena characterizing the cylindrical configurations of the nanocylinders can be realized using a relatively simple structure composed of three nanocylinders and there is no need to further increase a number of the scatterers (nanocylinders).

A rigorous self-contained formulation for analyzing electromagnetic scattering by a grating of plasmonic nanorods (Ag) coupled to a magneto-optical slab is presented. Bi-substituted gadolinium iron garnet is considered as the magneto-optical material. We measured the dielectric permittivity of the iron garnet and utilized the experimental data in our analyses. The method uses the Lattice Sums technique combined with the generalized reflection matrix approach. Using the method, the spectral response in reflectance as well as near-field distributions at resonance wavelengths have been numerical studied. Special attention has been paid to the coupling mechanism between the plasmonic grating and the magneto-optical slab. Physical insight is given to the strong field enhancement inside the magneto-optical material due to coupling with the plasmonic grating. Generalization of the method to the multilayered sandwiched structures, where the metal layer supporting surface plasmons is in contact with a layer possessing magnetically induced anisotropy, is straightforward. Such a combination enables one to achieve a multifold increase in sensitivity when compared with a system having just one nonmagnetic metal layer.

The scattering of TE polarized plane wave by metal-coated dielectric nanocylinders is investigated with a particular emphasis on the enhancement of the near fields. If the wavelength of illumination is properly chosen, two unique near field distributions can be excited through the surface plasmon resonances. The enhanced near fields are localized along the inner or outer interface of the coating metal, being dependent on the wavelengths. It is shown that the scattering cross-section of the nanocylinders is also enhanced when the illuminating field resonates to the surface plasmons of the structures.

Doubled-sided grating structures including two identical single-layered metal gratings separated by a dielectric layer exhibit enhanced optical transmission in the visible region for transverse magnetic polarized light. The maximum transmission (71%) is attributed to a resonance of magnetic polaritons while the minimum one (5%) is found to be caused by surface plasmons between metal and dielectric layers. The transmission resonance of the grating structures is analyzed by varying their geometrical parameters and materials in order to evaluate different potential applications such as tunable optical filters, polarizers, and self-suspended-type plasmonic sensors.

During the last few decades, an extensive research effort has been aimed at studying and developing novel structures based on the photonic crystals composed of the multilayered arrays of periodically distributed circular rods. A photonic crystal with a complete bandgap has been used to localize electromagnetic waves to specific arrays and to guide the propagation of electromagnetic waves along certain directions at restricted frequencies. After this discovery, photonic crystals have inspired great interest because of their novel scientific and engineering applications in guiding devices for controlling the propagation of light. Various analytical and numerical methods have been developed to analyze the photonic crystal waveguides made by removing a row of either air columns or dielectric rods that result in multimode guiding [1, 2]. Recently, scientific attention has been paid to the possibility to efficiently guide electromagnetic waves along a chain formed by periodically distributed scattering elements (a simple single-layered structure) [3, 4]. A simplicity of design and fabrication could be considered as the main advantage of this structure. However, in order to validate its good guiding properties, detailed theoretical and numerical studies are needed. In this regard, we propose a Fourier series expansion method as an efficient method to study the guiding modes and leaky modes of infinite chain of periodically distributed circular rods [5]. In the proposed method a fictitious periodicity in the transverse direction (in the upper and lower regions of the guiding structure) is introduced and the original waveguide is approximated by one period of the periodic waveguide array. The electric and magnetic fields are expanded in a Fourier series and the problem is reduced to the set of linear equations for the Fourier coefficients. Based on the Fourier series expansion method we have numerically calculated the real and imaginary values of the propagation constant associated with the guiding and leaky modes, respectively. The results for the real value of the propagation constant has been compared with the results obtained based on the Lattice Sums technique and the excellent agreement has been observed between these two methods. Several numerical results have proofed the accuracy and validity of the propose formulation. Although in our studies we consider the circular rods to be the pure dielectric (without intrinsic loss), the problem can be easily generalized to study the structure composed of the periodically distributed plasmonic nanocylinders having a complex dielectric permittivity.

Interaction of light with the metallic nanostructures gives rise to various novel effects in photonics and optoelectronics [1]. Research of surface plasmons and their excitation by light is of particular interest in the studies of metamaterials, optical antennas, plasmonic sensors, and plasmonic crystals. The enhanced surface plasmon resonance in noble metallic systems at optical frequencies is expected to be a promising issue for realizing excellent scatterers and absorbers of the visible light. The surface plasmons characterize the unique response in collective motions of electrons on a metal-dielectric interface, which is allowed when the permittivity of the metal is negative for the wavelength of excitation. Recently, much attention has been paid to the light scattering from periodic nanowires coupled to a layered dielectric structure [2] for their applications to optical sensors, imaging, and integrated devices.

Light scattering by a grating made of the Ag nanocylinders onto a dielectric substrate is investigated using an accurate and rigorous formalism based on a recursive algorithm combined with the lattice sums technique. Physical insight is given to the localization of the field along the interfaces of the Ag nanocylinders, to the strong reflected field by the grating and the field enhancement at the surface of the dielectric substrate. The accuracy of the numerical analysis has been validated based on the principle of the energy conservation.

A semi-analytical approach for a periodic planar array formed by a finite number of circular cylinders is presented using a model of layered cylindrical arrays. The method consists in extracting the reflection and transmission matrices of a cylindrically periodic array of circular cylinders and then obtaining the characteristics of layered structures by using a recursive formula.

A semi-analytical approach for analyzing two-dimensional electromagnetic scattering by layered cylindrical arrays of circular rods periodically distributed along concentrically layered circular rings is presented. The method uses the T-matrix of a circular rod in isolation, the reflection and transmission matrices of a cylindrical array expressed in terms of the cylindrical harmonic waves as the basis and the generalized reflection and transmission matrices for a layered cylindrical structure. Using the method, the scattering of plane waves impinging on the cylindrical arrays from the exterior region and the radiation from a line source located inside the cylindrical arrays are numerically investigated. Numerical examples demonstrate that the layered cylindrical arrays are effective for forming a directed beam in the scattered and radiated fields.

Two simple single layer single feed cross slot patch antennas with air dielectric (er = 1) substrate providing multiple frequency operation is proposed.At first a cross slot rectangular patch antenna providing quad frequency operation is proposed and experimentally studied. The measured quad frequencies are 1.93, 2.57, 3.18, and 3.56 GHz. Another cross slot trapezium patch antenna providing quad frequency operation is proposed and experimentally studied. The measured quad frequencies are at 1.43, 1.81, 2.97, and 3.58 GHz. Trapezium patch antenna is found to be more compact in size and as well as reduction in resonant frequency compared to rectangular patch antenna. Measured values are in good agreement with simulated results. The measured radiation patterns at each measured resonant frequency are also shown. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:612–615, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25765

A semi-analytical approach for analyzing the electromagnetic radiation of a line source in cylindrical electromagnetic bandgap (EBG) structure is presented. The cylindrical structure is composed of circular rods periodically distributed along concentrically layered circular rings. The method uses the T-matrix of a circular rod in isolation, the reflection and transmission matrices of a cylindrical array expressed in terms of the cylindrical waves as the basis, and the generalized reflection and transmission matrices for a layered cylindrical structure. Using the proposed method, the radiated field from a line source placed inside a three-layered cylindrical EBG structure with defects is investigated. The defects are created by removing the particular circular rods from each circular ring. The structure is prominent from the viewpoint of flexible design of the directive antennas. Numerical examples demonstrate that the cylindrical EBG structures are very effective at forming and controlling the directed beam in the radiated fields.

A rigorous semi-analytical approach for the scalar field in a microstructured optical fiber, which is formed of layered cylindrical arrays of circular rods symmetrically distributed on each concentric cylindrical layer, is presented. The method uses the T-matrix of a circular rod in isolation and the generalized reflection and transmission matrices of cylindrical arrays. Numerical examples of the mode index for three-layered hexagonal structure of circular air holes are demonstrated and compared with those obtained by a variational method.

Directivity of radiation from a localized source coupled to electromagnetic crystals is investigated theoretically using a two-dimensional model. The closed form expression for the far field of radiation is derived and used to examine two primary factors governing the directivity. It is shown that the directivity is uniquely characterized by the transmission windows of the electromagnetic crystals in the frequency and angular spectral domains and the Fabry-Perot resonance condition for the radiated field in the space surrounding the source.

A semi-analytical approach for a specific microstructured fiber, which is formed by layered cylindrical arrays of circular rods in a homogeneous background medium, is presented. The M circular rods are symmetrically distributed on each of the N -concentric circular cylindrical surfaces The method uses the T -matrix of a circular rod in isolation, the reflection and transmission matrices for a cylindrical array, and the generalized reflection and transmission matrices for a cylindrically layered structure.

The Fourier series expansion method is a useful tool to approach the problems of discontinuities in optical waveguides, and it applies to analyze the Floquet-modes of photonic crystal waveguides. This paper shows that the Floquet-mode calculation with large truncation order is limited and explains the reason. Furthermore, two techniques of the formulation are presented to relieve this limitation. One of them is a use of the symmetric properties of the Floquet-modes, and another is a use of the Rayleigh quotients to improve accuracy of eigenvalue calculation. They are validated by numerical experiments.

A theoretical analysis of the cladding modes is presented for an asymmetric dual-core fiber that consists of a primary core near the fiber axis and a secondary core. Numerical examples are given to demonstrate that the approximation of a two-layer fiber geometry is inadequate to describe the accurate modal properties of the cladding modes. It is shown that the field distributions of the cladding modes are dependent on the azimuthal angle under the presence of two cores. The maximum field intensities are located away from the fiber axis with a shift in the local maxima in the primary core toward the secondary core. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 507–510, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24066

A problem of coupling between conventional dielectric waveguides and a two-dimensional photonic crystal waveguide is analyzed, using the Fourier series expansion method combined with the absorbing boundary condition of a perfectly matched layer (PML). A novel structure for the input and output ends of the photonic crystal waveguide is proposed to increase the coupling efficiency. Numerical examples are demonstrated and discussed to validate the effectiveness of the proposed structure.

This study presents theoretical and experimental investigations on novel, compact, single layer and single probe-fed rectangular microstrip patch antennas for dual and multi frequency operation. The novel design is achieved by cutting two rectangular slots at one side of the patch antenna. Compared with the conventional rectangular patch antenna, our antenna can achieve reduction in patch size up to 85%. Dual frequency operation has also been achieved effectively by just adjusting the feed position of a conventional rectangular patch antenna. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 961–965, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23255

A novel formulation of radiation from a localized line source placed in two-dimensional photonic crystals consisting of layered periodic arrays of parallel circular cylinders is presented. The method employs the spectral domain approach. The spectral response of the photonic crystals to the line source excitation is calculated using the lattice sums, the T-matrix of a circular cylinder, and the generalized reflection and transmission matrices of the layered system. The far-zone radiated field is obtained using the conventional asymptotic method to the spectral response. The radiation patterns of the localized line source sandwiched by two photonic crystals are numerically studied.

We analyzed the frequency and quality factor of microcavities on a two-dimensional photonic crystal, using a Fourier series expansion method combined with perfectly matched layers (PMLs). Numerical examples are demonstrated and discussed to show that the resonant frequency and the quality factor Q values can be calculated by the present method using PMLs.

A semi-analytical method to model post-wall waveguides is presented. The approach is based on the model of two-dimensional photonic crystal waveguides formed by layered periodic arrays of circular rods. The propagation constant of the fundamental TE mode and the effective waveguide width as an equivalent rectangular waveguide are analyzed using the proposed method.

A rigorous electromagnetic theory is developed to analyze multiport waveguide junctions with artificial inclusions formed of the conducting strips and dielectric layers. The method is based on the Fourier transform technique combined with the mode matching method technique that takes into account the edge conditions in vicinity of the strip edges. The scattering characteristics of a 3-port junction are discussed with the numerical examples for the SWR maps, the power reflection and transmission coefficients, and the 2D plots of near fields distributions inside the junction area. A strategy of optimize matching properties of the 3-port waveguide junctions is also presented.

Electromagnetic crystals formed by vertical full posts stacked in a rectangular waveguide are analyzed using the image theory and the lattice sums technique. It is shown that the frequency response of the crystals consisting of circular posts can be obtained by a simpler matrix calculus based on the one-dimensional lattice sums, the T-matrix of a circular cylinder in free space, and the generalized reflection and transmission matrices.

A rigorous and simple method is proposed for analyzing guided modes of metallic electromagnetic crystal waveguides. The method is a combination of generalized reflection and transmission matrices and the mode-matching technique. Fast convergence, low computer cost, and high calculating precision are main advantages of the proposed method. This method can easily avoid the relative convergence phenomena than a classical mode-matching method, and the proposed formulation is very suitable to analyzing multilayered problems with very low computer cost. The existence of H-polarized modes in metallic electromagnetic crystal waveguides has been verified.

A full-wave method for modal analysis of two-dimensional photonic-crystal waveguides consisting of layered arrays of rectangular cylinders is presented. The mode propagation constants and the mode field profiles can be derived by an improved Fourier series method, which is of very simple form, and is always suitable for all the arrays of arbitrary profiles, any depth, and any permittivity. The dispersion equation is expressed by using the generalized reflection matrices for space harmonic waves. The validity of the proposed method has been confirmed by comparison with other methods. Numerical examples of the dispersion characteristics and field distributions are presented for the lowest TE and TM modes of several waveguides in different structures. This method can analyze not only the propagation properties of waveguides, but also their loss natures.

Electromagnetic scattering from two-dimensional photonic crystals with two-dimensionally periodic defects is analyzed using a model of multilayered periodic arrays of parallel circular cylinders. The reflectance of the photonic crystals of finite thickness, which are free-standing or embedded in a dielectric slab, is obtained in terms of the lattice-sums, the T-matrix of a circular cylinder, and the generalized reflection matrix for a layered system. Numerical examples demonstrate that the refection and transmission bands of the crystals are reformed by introducing the periodic defects and their band natures are very sensitive to the polarization of excitation and the relative position of the defect element within a unit cell.

A rigorous and simple method of analyzing scattering and absorbing characteristics of multilayered gratings embedded in a dielectric slab has been proposed. The method combines a generalized scattering matrix with a lattice sums matrix and a T-matrix of an isolated single cylinder instead of the aggregate T-matrix. The validity of the present method has been confirmed by several numerical experiments and comparisons with other published results. Numerical examples show that the absorbing characteristics become very complex and are not linear with the decreasing of cylinders’ conductivity, when the arrays are stacked to a multilayered structure and are embedded in a dielectric slab.

The two-dimensional electromagnetic scattering by layered periodic arrays of circular cylinders embedded in a ferrite slab magnetized in the direction parallel to the cylinder axis are analyzed, using the lattice sums technique, the T-matrix of cylindrical objects, and the generalized reflection and transmission matrices for a layered system. It is shown that the reflection and transmission properties of the embedded arrays are accurately calculated by a simple matrix calculus based on the one-dimensional lattice sums and the T-matrix of the circular cylinder isolated in the magnetized ferrite slab. Numerical examples for the frequency response in the reflectance and transmittance are presented, and the switching properties of the embedded arrays controllable by the applied magnetic field are discussed.

Leaky characteristics of dielectric ridge guide with triangular and trapezoidal cross section are analyzed by a method that combines the mode matching procedure with the staircase approximation and multimode microwave network theory. Our emphasis in this paper is on the parametric effects of cross section profile on leakage and propagation properties of the ridge guide. Some numeral results with their explanations are given for practical reference.

Loss and dispersion characteristics of groove guide are two practically important factors in the design for millimeter wave system consisting of groove guide. In this paper, a new method is presented for analyzing loss and dispersion characteristics of the groove guides with arbitrary groove cross-sections. The method is based on the combination of an equivalent active transmission line equation and the staircase approximation. Numerical results of dispersion and attenuation properties for some groove guides with different groove profiles are given. The effectiveness and practicality of the present analysis are confirmed by the data given in the literature.

A rigorous and simple method is described for analyzing guided modes of metallic electromagnetic crystal waveguides consisting of conductive circular cylinders. The mode propagation constants and the mode field profiles can be accurately obtained by a simpler matrix calculus, using T-matrix of an isolated circular cylinder, the one-dimensional lattice sums technique, and generalized reflection matrices. Fast convergence, low computer cost, and high calculating precision are the main advantages of this method. Numerical examples of the dispersion characteristics and field distributions are presented for lowest E- and H-polarized modes of several metallic electromagnetic crystal waveguides and coupled two-parallel electromagnetic crystal waveguides of conductive circular cylinders in a background free space. The existence of H-polarized modes in metallic electromagnetic crystal waveguides has been verified.

This paper describes a method of efficient and accurate analysis of the problems of scattering and guiding of wave by two-dimensional electromagnetic crystals consisting of multilayered periodic arrays of circular cylinders, making use of the Lattice Sum, the T-matrix, the generalized reflection matrix, and the scattering matrix. According to this method, various characteristics of two-dimensional electromagnetic crystals can be calculated by a simple matrix algorithm. The method can handle cases in which several cylinders of different sizes and materials are contained within the unit cell of the array. Although the periodic spacing of the cylinders in the array must be fixed for all array layers, the size and material of the cylinders in the array and the distance between the array layers can be chosen freely. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 88(9): 19–28, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20182

is shown in Figure 12. Again, it is found that the error sharply increases when the segments with both large size and large radius are used. CONCLUSION This paper has investigated the accuracy of a wire-grid model using MoM computation. The mixed-potential electric-field integral equation (MPIE) is formulated to analyze electromagnetic scattering of the PEC bodies with the wire-grid model, where the triangular basis function and the sinusoidal basis function used in NEC2 are implemented, respectively. The accuracy of the model is explored via error evaluation of the calculated near-zone scattering electric field in the analysis of the sphere and plate scattering, where the error function takes the error from the magnitude, phase, and polarization of the calculated fields into account. The results indicate that the wire-grid model in combination with the MoM algorithm with the triangular basis function can accurately analyze electromagnetic problems. This model was optimized and the minimum error was reached when the coefficient of the radius was about 0.9, regardless of the size of the segments. The slight change of the radius near the optimal radius hardly influenced the accuracy of this model. However, the wire-grid model combined with the MoM with the sinusoidal basis function used in NEC2 resulted in sufficiently high error such that the EM problem cannot be simulated with it.

A rigorous and simple method for analyzing a rectan- gular-groove guide using a Fourier-transform technique, which takes the field singularities at the edge of the guide into consideration, is presented. The convergence of the solutions is very fast and the ac- curacy improves significantly. It is shown that a mode-propagation constant with five-figure accuracy is obtained by solving a 7 7 matrix equation. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 41: 388 -392, 2004; Published online in Wiley Inter- Science (www.interscience.wiley.com). DOI 10.1002/mop.20148

—Rigorous and fast convergent analysis of a coupler slotted in common wall between two dissimilar rectangular waveguides is described by a mode-matching method combined with Fourier transform technique and consideration of the singularity of electromagnetic field around edges. Comparing with a conventional mode-matching method, the present method has two advantages. One is that it can avoid the usage of the dyadic Green’s function, the other is that it can overcome the relative convergence problem. The consideration of the field singularity has greatly improved the convergence and the calculated accuracy of a solution. This analysis is rigorous and the computer cost is very low.

A very efficient and accurate method to characterize electromagnetic scattering by multilayered periodic arrays of circular cylinders is presented, using the lattice sums technique, the aggregate T-matrix algorithm, and the generalized reflection and transmission matrices for a layered system. The method is quite general and applies to various configurations of two-dimensional or three-dimensional periodic arrays. The unit cell of array can contain two or more cylinders, which may be dielectric, conductor, gyrotropic medium, or their mixture with different sizes. The periodic spacing of cylinders along each array plane should be same over all layers, otherwise the cylinders in different layers may be different in material properties and dimensions.

Three-dimensional optical waveguides with an arbitrary cross section and a periodic configuration have been important as optical IC elements. However, it is not always easy to obtain highly accurate solutions for them without respect to the number of periods. In this paper, the Fourier series expansion method, improved for accurate numerical analysis independently of the number of periods introducing Floquet's theorem, is applied to a fiber grating and various thin-film optical waveguides with index-modulation-type periodic structures and rectangular cross sections. The wavelength characteristics of the transmitted and reflected powers of the guided mode and the radiation field are derived at each period (40 to 1000). As a result, the wavelength characteristics of the power are made clear for periodic optical waveguides of embedded type and raised type with a glass or semiconductor substrate, including inhomogeneous cases. The algorithm thus proves to be useful for detailed analysis of various three-dimensional periodic optical waveguides. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 86(12): 22–31, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.10171

Three-dimensional optical waveguides with periodic structure promise to play an important role in optical IC, and more accurate analysis of such waveguides is required. In this paper, an improved, more accurate Fourier series expansion method for an arbitrary number of grating periods making use of Floquet's theorem is applied to the numerical analysis of lamellar grating-type periodic optical waveguides with rectangular cross section (glass substrate). In the numerical results, the characteristics of the reflected and transmitted powers of the guided and radiation fields versus wavelength are investigated when the depth of the grating grooves and the number of grating periods are varied. The effects of the groove depth and the number of periods on the powers of each mode are elucidated and the appropriate parameters for dominant guided mode propagation in the periodic waveguide are identified. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 149(2): 1–9, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20034

The Fourier series expansion method is applied to realize an accurate full-vectorial analysis of the problem of a step-index optical fiber connected to an inhomogeneous embedded optical waveguide with rectangular cross section, using periodic boundary conditions in both transverse directions. Using this method, the Maxwell's equations in the waveguide system are reduced to a simple eigenvalue problem of a linear system for the Fourier coefficients. Then the behavior of the transmitted and reflected powers of the guided and radiation modes is clarified for each gap distance and transverse shift between the two waveguides, and compared with the cases of the homogeneous embedded waveguide and different transverse refractive index variations. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 14–18, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11272

A numerical approach for transition problems in optical waveguides is presented, with the use of the Fourier-series expansion method combined with the absorbing boundary condition by a perfectly matched layer (PML). The optical propagation along a transition is described by a simple matrix algebra. The numerical examples demonstrate that the radiation modes with wider propagation angle are strongly attenuated in the presence of PML, and hence unwanted interference of the boundary-reflected radiation field to the guided wave field is suppressed. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 422–426, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10482